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Chapter 5: Q18 (page 175)

For exercises, 14-18 write paragraph proofs.

Given: parallelogram KGLJ; FK=HL.

Prove: FGHJ is a parallelogram.

Short Answer

Expert verified

It is proved that the quadrilateral FGHJ is a parallelogram.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Description of step.

It is being given that KGLJ is a parallelogram.

In a parallelogram, both diagonals bisect each other.

Therefore, in the parallelogram KGLJ, both diagonals KL and JG intersect each other at the point O.

Therefore, KO=LOand JO=GO.

03

Step 3. Description of step.

It is also being given that FK=HL.

Therefore, it can be noticed that:

FK=HLFK+KO=HL+KOFK+KO=HL+LO鈭�KO=LOFO=HO

Therefore, it can be noticed that JO=GOand FO=HO.

Therefore, it can be seen that the diagonals FH and JG are bisecting each other at point O.

Therefore, the quadrilateral FGHJ is a parallelogram.

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